Equation of a Mobius Strip

By Brad Rodgers (P1930) on Wednesday, December 27, 2000 - 07:16 pm :

Does anyone know of an equation z(x,y)=... that describes the mobius strip.

Thanks,

Brad

By Maria Jose Leon-Sotelo Esteban (T3819) on Saturday, December 30, 2000 - 07:38 am :

The parametric equation for an Mobius strip are:

$f (u, v) = (\cos (u) + v \cos (u / 2) \cos (u), \sin (u) + v \cos (u / 2) \sin (u), v \sin (u / 2))$

$0 \leq u \leq 2 π$ ; $- 0.3 \leq v \leq 0.3$
Maria Jose de Leon-Sotelo.

By Brad Rodgers (P1930) on Saturday, December 30, 2000 - 06:05 pm :

Ah, thanks! That seems to work to make the graph. Unfortunately, I don't understand parametrics very well, (I was barely able to get through finding the equations to put in the graph-for some reason you have to put it in matrices) so I don't see why the graph works very well. Is there a way to translate that into rectangular (Cartesian) coordinates? The formula you gave does work very well though.

Brad

By Anonymous on Tuesday, January 2, 2001 - 05:27 pm :

The elimination of u and v in the parametric equations gives:

$begin{displaymath}z = yBiggl(frac{sqrt{x^2+y^2}-1}{sqrt{x^2+y^2}+x}Biggr) end{displaymath}$

Maria Jose.